Phil Edwards answered the OP's question very succintly. But let's clear up one thing: as far as 'trad., arr.' goes, if I register my own recording of a song as such, it gives me no rights whatsoever with respect to the ownership of that traditional song, or over other people singing or recording it. What it does give me is the right to a slice of the loot if my recording gets played on radio or TV, etc. I fail to see why that is in some way theft, as some of the previous discussion seems to suggest (John Reilly / 'Maid & Palmer' is a special case, IMO). Nor do I understand why (as John P asserts) setting a trad. lyric to a melody not usually associated with it shouldn't be regarded as a new arrangement.

I can, however, think of examples of traditional songs being claimed as original compositions by certain artists. Very bad form.

I can also think of instances in which an artist has credited their version of a song to a previous traditional arrangement by another artist, because the second version borrowed instrumental ideas as well as just words and tune. And I can think of instances in which the same thing has happened, but without proper credit being given.